maintenance / support
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support
The financial support that a person is legally required to provide for another person's living expenses, especially for children or former spouses.
Nach der Scheidung muss er monatlich Unterhalt für seine beiden Kinder zahlen.
After the divorce, he has to pay monthly support for his two children.
maintenance
The costs incurred for a person's living needs or for the upkeep of something (e.g., a house or car).
Der Unterhalt für ein so großes Anwesen ist finanziell sehr aufwendig.
The maintenance of such a large estate is very expensive.
'Der Unterhalt' (maintenance/support) derives from the verb 'unterhalten'. This verb can mean to provide for someone financially ('eine Familie unterhalten' — to support a family) or to keep something in good condition ('ein Haus unterhalten' — to maintain a house).
Es ist teuer, ein so altes Auto zu unterhalten.
It is expensive to maintain such an old car.
You can recognize the meaning from the context: If it is about family, divorce, and children, financial support (m01) is meant. If it is about houses, cars, or technology, the costs of maintenance (m02) are meant.
Sie streiten vor Gericht um den Unterhalt für die Kinder.
They are fighting in court over support for the children.
In a legal context, 'Unterhalt' (support) is often used with the verbs 'zahlen' (to pay), 'bekommen' (to receive), 'fordern' (to demand/claim), or 'leisten' (to provide). The person who receives the money is named with the preposition 'für' (for).
Er ist gesetzlich verpflichtet, Unterhalt für seine Ex-Frau zu zahlen.
He is legally required to pay support for his ex-wife.
The noun 'der Unterhalt' is used almost exclusively in the singular, even when it refers to the costs for several things or people. The plural 'die Unterhalte' is very rare.
Der Unterhalt für das Haus und das Auto wird immer teurer.
The maintenance for the house and the car is getting more and more expensive.
support
Both words can refer to financial help with a person's living expenses. Unterstützung is the more general term and may be provided voluntarily or for various reasons; Unterhalt usually emphasizes a payment owed within a family or required by law. For a specific payment of this kind, Unterhalt is therefore more precise.
Nach der Trennung zahlt der Vater regelmäßig Unterhalt für sein Kind.
After the separation, the father regularly pays child support.
Meine Eltern geben mir während des Studiums finanzielle Unterstützung.
My parents provide me with financial support during my studies.
